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Simplifying 3n(4n2 + -1n + 5) = 0 Reorder the terms: 3n(5 + -1n + 4n2) = 0 (5 * 3n + -1n * 3n + 4n2 * 3n) = 0 (15n + -3n2 + 12n3) = 0 Solving 15n + -3n2 + 12n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(5 + -1n + 4n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(5 + -1n + 4n2)' equal to zero and attempt to solve: Simplifying 5 + -1n + 4n2 = 0 Solving 5 + -1n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -0.25n + n2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.25n + -1.25 + n2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.25n + n2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.25n + n2 = 0 + -1.25 -0.25n + n2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.25n + n2 = -1.25 The n term is -0.25n. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25n + 0.015625 + n2 = -1.25 + 0.015625 Reorder the terms: 0.015625 + -0.25n + n2 = -1.25 + 0.015625 Combine like terms: -1.25 + 0.015625 = -1.234375 0.015625 + -0.25n + n2 = -1.234375 Factor a perfect square on the left side: (n + -0.125)(n + -0.125) = -1.234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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